Renaming or copying files and folder using NERDTree on Vim. Is it possible?

Press m on the node you want to then select (m)ove the current node. Moving is the same as renaming.

NERDTree Menu. Use j/k/enter and the shortcuts indicated
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> (a)dd a childnode
  (m)ove the curent node
  (d)elete the curent node
  (c)copy the current node

https://github.com/scrooloose/nerdtree/blob/master/doc/NERDTree.txt, the latest version has it:

2.3. The NERD tree menu NERDTreeMenu The NERD tree has a menu that can be programmed via the an API (see |NERDTreeMenuAPI|). The idea is to simulate the "right click" menus that most file explorers have. The script comes with two default menu plugins: exec_menuitem.vim and fs_menu.vim. fs_menu.vim adds some basic filesystem operations to the menu for creating/deleting/moving/copying files and dirs. exec_menuitem.vim provides a menu item to execute executable files.